A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Size bounds for dynamic monopolies
Discrete Applied Mathematics
Optimal irreversible dynamos in chordal rings
Discrete Applied Mathematics - special issue on the 25th international workshop on graph theoretic concepts in computer science (WG'99)
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
Theoretical Computer Science
Spreading of messages in random graphs
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Stable sets of threshold-based cascades on the erdős-rényi random graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Triggering cascades on undirected connected graphs
Information Processing Letters
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
Constant thresholds can make target set selection tractable
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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In a distributed computing environment a faulty node could lead other nodes in the system to behave in a faulty manor. An initial set of faults could make all the nodes in the system become faulty. Such a set is called an irreversible dynamo. This is modelled as spreading a message among individuals V in a community $G=\left( V,E\right) $ where E represents the acquaintance relation. A particular individual will believe a message if some of the individual's acquaintances believe the same and forward the believed messages to its neighbours. We are interested in finding the minimum set of initial individuals to be considered as convinced, called the min-seed, such that every individual in the community is finally convinced. We solve for min-seed on some special classes of graphs and then give an upper bound on the cardinality of the min-seed for arbitrary undirected graphs. We consider some interesting variants of the problem and analyse their complexities and give some approximate algorithms.